Problem: Dagogo uploads $3$ videos on his channel every month. Each video averages $15$ minutes in length and gets an average of $150{,}000$ new views. The average ratio of likes-to-views of Dagogo's videos is $1:5$. Dagogo wants to reach a total of $9{,}000{,}000$ views on his channel. Assuming these rates continue, for how many months does Dagogo need to upload videos to get to $9{,}000{,}000$ views on his channel?
Solution: There can be many ways to solve this problem. Here, we will do this by thinking about units. Let's say it will take Dagogo $x\,\text{months}$ to reach $9{,}000{,}000\,\text{views}$. How can we relate these two quantities with an equation? $\begin{aligned} x\,\text{months}\cdot y\,\dfrac{\text{views}}{\text{month}}=9{,}000{,}000\,\text{views} \end{aligned}$ So in order to find the number of months $x$, we need to figure out the value of $y$, which is the rate of views per month. Notice what other information we are given: $3\,\dfrac{\text{videos}}{\text{month}}$ $15\,\dfrac{\text{minutes}}{\text{video}}$ $150{,}000\,\dfrac{\text{views}}{\text{video}}$ $0.2\,\dfrac{\text{likes}}{\text{view}}$ Which of these quantities can help us calculate a rate whose units are $\dfrac{\text{views}}{\text{month}}$ ? We can combine the following quantities: $\begin{aligned} 3\,\dfrac{\cancel\text{videos}}{\text{month}}\cdot150{,}000\,\dfrac{\text{views}}{\cancel\text{video}}=450{,}000\,\dfrac{\text{views}}{\text{month}} \end{aligned}$ Now we can plug that in the original equation: $\begin{aligned} x\,\text{months}\cdot 450{,}000\,\dfrac{\text{views}}{\text{month}}&=9{,}000{,}000\,\text{views} \\\\ x\,\text{months}&=\dfrac{9{,}000{,}000}{450{,}000}\,\cancel\text{views}\cdot\dfrac{\text{months}}{\cancel\text{view}} \\\\ x\,\text{months}&=20\,\text{months} \end{aligned}$ In conclusion, to get to $9{,}000{,}000$ views, Dagogo needs to upload videos for $20$ months.